Gleason’s Game

A two-person zero-sum game invented by Andrew Gleason in the early 1950’s has a very simple description and yet turns out to be quite difficult to solve. This game is a stochastic game with an information lag for both players. No strategy with a bounded memory of past moves can be optimal. Yet using the notion of generalized subgames, we show that there exist optimal strategies of a simple nature based on functions easily approximable by standard methods of computation for stochastic games. 1. Description of the game. Two players, Andy and Dave, move a counter around a three node board. The nodes are arranged in a circle and are labeled +1, +2, and −3. Initially the counter rests on node +1 and Andy starts.